ABSTRACT
Previously, when discussing the properties of one parameter discrete model of genetic diversity (M.Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887-894 (1998)), we took into account Hamming distance distribution only between precursor and arbitrary descendant sequences. However, really there are sets of sequence populations produced during amplification process. In the presented work we have investigated Hamming distance distributions between sequences from different descendant sets produced in the frame of one parameter discrete model. Two basic descendant generation operators (so called amplifiers) are introduced: 1) the last generation amplifier, L, which produces descendants with precursor elimination; 2) all generations amplifier, G, which produces descendants without precursor elimination. Generalization of one-parameter discrete model for the case when precursor sequences do not coincide are carried out. Using this generalization we investigate the distribution of Hamming distances between L- and G-generated sequences. Basic properties of L and G operators, L/G-choice alternative problem have been discussed. Obtained results have common theoretical significance, but they are more suitable for high level genetic diversity process (for example, HIV diversity).
Subject(s)
Genetic Variation , Models, Genetic , MathematicsABSTRACT
With the help of previously introduced enumeration procedure (M.Yu. Shchelkanov, A.N. Yudin, A.V Antonov, N.S. Starikov, A.A. Vedenov, E.V. Karamov, J. Biomol. Struct. Dyn. 15, 217-229 (1997)) and probability distribution function for the enumeration after some substitution steps (M.Yu. Shchelkanov, L.A. Soinov, V.V. Zalunin, D.A. Gumennyi, A.N. Yudin, A.A. Natan, V.B. Kireev, E.V. Karamov, J. Biomol. Struct. Dyn. 15, N 4, (1998)) we have demonstrated that dependencies of replication acts number on Hamming distance are identical for one-parameter discrete models of both direct and parallel genetic diversity.
Subject(s)
Genetic Variation , HIV Envelope Protein gp120/genetics , Models, Molecular , Models, Statistical , Peptide Fragments/genetics , Evolution, Molecular , HumansABSTRACT
One-parameter discrete model estimating genetic distance between precursor and descendant nucleotide sequences after several steps of substitution acts is developed. This model based on the previously introduced symbol sequences enumeration procedure (M.Y. Shchelkanov, A.N. Yudin, A.V. Antonov, N.S. Starikov, A.A. Vedenov, E.V. Karamov, J. Biomol. Struct. Dyn. 15, 231-241 (1997)) differs from Jukes-Cantor and Kimura models by the absence of the assumptions usual for continuous Markov's processes. Formula obtained with the help of our model are more preferable since they take into account multiple repetition substitution ability and they are correct in the entire admissible range of parameters.
Subject(s)
Globins/genetics , Mathematical Computing , Models, Genetic , Animals , Chickens , RabbitsABSTRACT
In the previous work (M. Yu. Shchelkanov, A. N. Yudin, A. V. Antonov, N. S. Starikov, A. A. Vedenov, E. V. Karamov, J. Biomol. Struct. Dyn. 15, 217-229 (1997)) we have introduced the amino acid distribution function within HIV-1 taxons and Hamming-transformed Euclidean measures between their characteristics: consensus, subconsensus and sample mean. In this work the referred characteristics are used for hierarchical classification of amino acid sequences of gp120 V3 region belonging to different HIV-1 taxons. A comparative analysis of the results produced by various classification methods is carried out. Multidimensional scaling of distance matrix for the specified characteristics is used to visualize the pattern of HIV-1 variability.
